That would be assuming that my clone would magically be as matured as I am when he is created. If I were cloned, I would want my Clone to mature naturally, as if he were my son, just with the same DNA; well, maybe a few minor improvements, so he wouldn’t have to go through the same medical shit I had to, but still, basically a younger me with a second chance, to become everything I could have become if the circumstances had been a little different. It’s not like my parents did anything wrong; it’s just that there is always room for improvement.
My responsibility to my clone would be to provide for him, also pretty much any way a father would provide for his son (ideally; we all know good and bad parenting examples). I would have him learn useful basic skills like carpenting, blumbing, electrical works, and smithing, how to handle a firearm, basic martial arts, but mostly, which is more of my specialty, philosophy and ethics.
His responsibility would be to put the skills to good use, and build a legacy, and to teach the next clone what I have taught him. That way, I could live on forever 😉